A group of adults and kids went to see a movie. Tickets cost $$7.00$ each for adults and $$2.50$ each for kids, and the group paid $$39.00$ in total. There were $8$ fewer adults than kids in the group. Find the number of adults and kids in the group.
Answer: Let $x$ equal the number of adults and $y$ equal the number of kids. The system of equations is then: ${7x+2.5y = 39}$ ${x = y-8}$ Solve for $x$ and $y$ using substitution. Since $x$ has already been solved for, substitute ${y-8}$ for $x$ in the first equation. ${7}{(y-8)}{+ 2.5y = 39}$ Simplify and solve for $y$ $ 7y-56 + 2.5y = 39 $ $ 9.5y-56 = 39 $ $ 9.5y = 95 $ $ y = \dfrac{95}{9.5} $ ${y = 10}$ Now that you know ${y = 10}$ , plug it back into ${x = y-8}$ to find $x$ ${x = }{(10)}{ - 8}$ ${x = 2}$ You can also plug ${y = 10}$ into ${7x+2.5y = 39}$ and get the same answer for $x$ ${7x + 2.5}{(10)}{= 39}$ ${x = 2}$ There were $2$ adults and $10$ kids.